11,248 research outputs found
On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations
Considered herein are the generalized Camassa-Holm and Degasperis-Procesi
equations in the spatially periodic setting. The precise blow-up scenarios of
strong solutions are derived for both of equations. Several conditions on the
initial data guaranteeing the development of singularities in finite time for
strong solutions of these two equations are established. The exact blow-up
rates are also determined. Finally, geometric descriptions of these two
integrable equations from non-stretching invariant curve flows in
centro-equiaffine geometries, pseudo-spherical surfaces and affine surfaces are
given.Comment: 26 page
Statistical Constraints on the Error of the Leptonic CP Violation of Neutrinos
A constraint on the error of leptonic CP violation, which require the phase
to be less than for it to be distinguishable on a
cycle, is presented. Under this constraint, the effects of neutrino detector 's
distance, beam energy, and energy resolution are discussed with reference to
the present values of these parameters in experiments. Although an optimized
detector performances can minimize the deviation to yield a larger
distinguishable range of the leptonic CP phase on a cycle, it is not
possible to determine an arbitrary leptonic CP phase in the range of
with the statistics from a single detector because of the existence of two
singular points. An efficiency factor is defined to characterize the
distinguishable range of . To cover the entire possible
range, a combined efficiency factor corresponding to
multiple sets of detection parameters with different neutrino beam energies and
distances is proposed. The combined efficiency factors of various
major experiments are also presented.Comment: 9 pages, 5 figure
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